I would like to test this full model against a more restrictive model using difftest - fixing the factor loadings for x8, x9, x13, x14, and x15 to zero, to assess if dropping these five observed variables from the CFA estimation results in a significantly worse fit.

However, in the second step’s output, I received a message saying the following. So I’m wondering if perhaps I am not correctly understanding either what it means to fix a parameter to zero; or, if perhaps I am doing so incorrectly in Mplus:

“THE MODEL ESTIMATION TERMINATED NORMALLY THE CHI-SQUARE COMPUTATION COULD NOT BE COMPLETED BECAUSE OF A SINGULAR MATRIX.

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 16. THE CONDITION NUMBER IS -0.430D-17.”

I tested the full model against a more restrictive model using difftest - fixing the factor loading of n2 to zero, to examine whether discarding the observed variable (i.e., n2) from the CFA estimation cause a significantly better fit.

I got it. Many thanks for your help!! This is the new result: Chi-Square Test for Difference Testing Value 23.752 Degrees of Freedom 1 P-Value 0.0000

I think this is the right way for WLSMV, in Mplus, to examine whether discarding an observed variable from the CFA estimation cause a significantly better fit. If there is anything still incorrect in the process, please let me know.

It is a test of whether or not the n2 item is uncorrelated with not only the N factor but also every other factor and all other observed variables. The p-value of 0 says that this more restricted model is rejected.

You cannot do chi-2 difference testing when the two models have different sets of observed dependent variables (like with and without n2).

The more important point here, however, is that you want to take a quite different approach to answer your question "do we get a better CFA model fit without the n2 item?" I think the best way to answer that is to do an exploratory factor analysis. Your 5 factors should then show up clearly and you can see if the n2 item has a lot of significant cross-loadings on other factors and if it has a lot of significant residual correlations. If it does, it is an item that will contribute significantly to misfit of your the CFA model you postulate.

Thank you very much for your teaching!! I am surprised at the wrong of the approach that I learned from the other researchers using Mplus. I will introduce your valuable comment to the ones who took the same wrong approach as me.